Fast costate estimation for indirect trajectory optimization using Bezier-curve-based shaping approach

Abstract

In this study, a fast costate estimation method derived from the Bezier-curve-based shaping approach is proposed for indirect low-thrust transfer trajectory optimization. The trajectory is designed rapidly by means of the shape-based method, which can be discretized on the Gauss points and substituted into the discrete first-order optimal condition equation for costate estimation. The estimated costate at the starting point is substituted into the indirect method to solve the optimal control problem. The costate estimation performance for two interplanetary rendezvous missions from Earth to Mars and Earth to Dionysus is compared via random initialization and Newton's iteration method. The initial guesses for the transfer time are given by the Hohmann transfer and the Lambert two-pulse traversal search. The results show that the Lambert traversal search can provide a more accurate launch time estimation in the Bezier-curve-based shaping approach, which can estimate the costate for indirect trajectory optimization in an order of magnitude less time than that required by random initialization.